Screw top or other closures, such as lids, caps, covers, etc., rotatably couple with corresponding bottles, jars, and other containers providing means for securely covering the containers while still generally allowing the containers to be opened by a typical user without the need for a bottle opener, can opener, or other tool. For at least these reasons, screw-top closures have wide spread use in many product areas, such as health and beauty, household, automotive, pharmaceutical, food and nutrition, toys, pet care, office supplies, baby care, and many others. However, since often such containers are very tightly sealed at factories and/or are tightly resealed after use, a user may have trouble unscrewing the lid from the container. This issue is amplified when the overall diameter of the lid is particularly small or particularly large, such that it is difficult for the user to get a good handgrip on the lid. Troubles in opening rotatably covered containers is additionally increased when the user is weak, such as when the user is a child, is elderly, or is otherwise weakened by a medical condition.